oh my - the other day I said to my son... if only I could whistle for my horse!
and now I find out there's a horse flute?! How do I get one?
Looks like you use XBox so the v1.5 game content is available to you. I haven't looked to see where you are in-game, but if you've finished the Community Center, then a new questline will open up a new location in the game.
Once you proceed through the gameplay prompts and open up a larger portion of that game area, you will find a small location that's blocked, which tells you to continue finding things around the new locations, and will open up when you've found enough. In there will be a familiar face with a new set of quests, and one of the reward options is the Horse Flute. I've only just started playing this area out and followed imnvs' reward advice.
Edit: I previewed a little more of your posts and the v1.5 content isn't available on Android or iOS yet
so if that's your longest-played farm, you wont get the prompt for this new place yet. When it finally releases for your tablet, you'll be able to play it, but for now you'll have to play through your XBox farm to get the new stuff.
Oh darn, more playtime in Stardew Valley...